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As Andrew Robinson points out in his eminently informed and readable new book Cracking the Egyptian Code, when Napoleon Bonaparte's invasion force reached Egypt in 1798, it seemed "almost as interested in culture as in conquest". Bonaparte's Army of the Orient was driven by its leader's grandiose dreams of forging a road of conquest all the way to the Indus Valley, but the army was also, in the delightfully French manner, endlessly curious and hopeful of enlightenment along the way. A large and distinguished group of scholars, artists, non-military cartographers and scientists (including the mathematician Jean-Baptiste Joseph Fourier) - savants as they were called - accompanied the army, as intent on learning as their soldierly counterparts were on looting.

Their endeavours would lead to many fascinating developments - and the lavish official French governmental report, Description de l'Egypte, in nine enormous volumes - but none so world-changing as that of the so-called Rosetta Stone, discovered by a demolition squad of engineers in the fort village of Rashid in the Nile Delta in July, 1799. The stone was a 770-kilogram chunk of a larger stele, and on its face it bore three different sets of inscriptions, one of which was immediately recognised as ancient Greek. The officer whose men found the stele guessed at once that the three sections might be the same piece of prose in three different languages - one of which, Egyptian hieroglyphics, had been indecipherable prior to the discovery. The Stone was sent to Cairo for analysis.

It didn't stay there long. The conquering British confiscated it in 1801 and shipped it to London, where King George III ordered it housed in the British Museum. Despite repeated (and increasingly urgent) calls for its repatriation to Egypt, it has remained at the British Museum as its most popular item ever since. Plaster casts were sent to the universities at Cambridge, Dublin, Oxford and Edinburgh, and copies were sent all over Europe and America, and the attention of scholars in all those places was focused on the last line of the Greek section, which announces that the stele's proclamation is inscribed in hieroglyphics, "native" Egyptian (a kind of written version of the demotic values of the language), and Greek - what Robinson rightly calls "a sort of Holy Grail of decipherment".

Robinson is very kind (and very droll) about the various scholars who'd tried in vain to decipher Egyptian hieroglyphics without possessing that all-important Holy Grail, but once the stone was discovered and its contents disseminated in the first two decades of the 19th century, the race was on.

There were two main runners in that race, and they could scarcely have been more different from each other: in England, renowned polymath (physicist, doctor, linguist, translator) Thomas Young, about whom Robinson has already written the definitive modern biography - and Jean-Francoise Champollion, the subject of Robinson's latest work.

Young was born in a tiny village in Somerset in 1773 to neglectful Quaker parents who largely left him to fend for himself. He became a voracious autodidact who was often worried about his own precocity. "His early penchant for polymathy did him no favours in the professional world," Robinson writes, "and indeed provoked self-doubt and the worry that he would be viewed as a dilettante."

He was a pure creature of research whose "chief pleasures were intellectual: to read, to think, to write and occasionally to experiment, alone in his study". As a scientist, Einstein ranked him alongside Newton, but, Robinson tells us, he was "a paragon of modesty".

A far different creature was Champollion, the fiery-tempered son of a bookseller from Grenoble, although he shared with Young at least one telling fact: he, too, was largely responsible for shaping his own intellectual development. His mother often told the story of his miraculous nativity, how he was conceived when she was nearly 50 after she'd been marinated in wine by a local witch doctor named Jacquou the Magician; despite how often the story has been recycled by Champollion biographers, Robinson arches one eyebrow, Jeeves-style, and demolishes it with Olympian ease (he's likewise dismissive of the fanciful accounts of the first meeting between Champollion and Fourier, and a good many other myths that have accrued around his subject). He follows his "revolutionary" hero through all the trials of his early life, through his closeness with his older brother and distant relations with both parents, and into his dawning fascination with all things Egyptian. That fascination brought him - and many other scholars - to the Rosetta Stone.

The object of all this fascination had begun its life as a news bulletin. It dates from 196BC, from the ninth year in the reign of King Ptolemy V, citing his gratitude towards the ruling priestly class for their support during the ongoing, barely controlled chaos of his troubled minority on the throne. The priests wanted the literate citizenry (and the posterity that was never far from the ancient Egyptian mind) to note their intimate connection with the ruling house, and so they erected a massive stele with inscriptions in three languages: Greek, hieroglyphics, and the non-hieroglyphic "demotic" speech used throughout the country.

A vast gulf of time passed. At some point, the column was broken into big chunks, and those chunks were lost to the centuries. The archaeological world had plenty of hieroglyphics from ancient Egypt, but it had no working key to interpret them. The discovery of that key was made gropingly, in stages, by two men - Young and Champollion - and Robinson is at his best when he's carefully picking his way through the separate brilliances and shared controversy that brought the two men together in one of those photo-finish contests that so characterise the modern scientific era (the similarities to the awkward, overlapping co-discovery by Charles Darwin and Alfred Russel Wallace of evolution by natural selection are glaring).

Young got to work first. In the summer and autumn of 1814, he devoted his considerable energies to studying the Rosetta Stone in the hopes of deciphering it. He had a sound scientific mind, an excellent command of languages, and a deep capacity to hold large amounts of verbal and visual information in his short-term memory. Robinson considers this last factor the key difference between computer decoding programs and the human mind: "… in reality the human factor remains all-important - mainly because a human being can spot that two signs that objectively look somewhat different are in fact variants of the same sign," he writes. "but this task is extremely difficult for computers."

In 1819, Young published the "Egypt" article in the Encyclopaedia Britannica, in which he unveiled his work in cracking the Rosetta Stone code, including his crucial insight that the "demotic" portion of the stele was reproducing some parts of the hieroglyphic portion not through one-to-one translation but by adding occasional letters and symbols to substitute for purely conceptual cartouches.

Champollion published his Precis du systeme hieroglyphique des anciens Egyptiens in 1824, claiming: "I must say that in the same period, and without having any knowledge of the opinions of M le docteur Young, I managed to arrive, by a fairly certain method, at more or less similar results." He claimed not even to have seen Young's article until 1821 - which Robinson coyly refers to as "surely economical with the truth". But whatever insights Champollion might have gained from Young's work, even Robinson - Young's affectionate biographer - admits that Champollion took those insights and used them to penetrate far, far deeper into the mysteries of the Stone than Young had ever done. On September 14, 1822 Champollion burst into his brother's office in Paris, cried out "Je tiens mon affaire!" ("I have done it") and collapsed to the floor in mental exhaustion. The following October, he gave a lecture at the Academy of Inscriptions and Belles-Lettres to outline his discoveries for the first time in public. Young was in the audience, and the two met afterwards. To the disappointment of historical novelists everywhere, they appear to have chatted amiably.

Champollion's book about his discoveries, Lettre a M Dacier, was published the following month and permanently cemented its author's fame as the man who broke the Rosetta code and unlocked the stubborn mysteries of a vanished civilisation.

Young was at first silent, then gracious, then baffled, and finally acrimonious about Champollion's tacit insistence that he'd arrived at his breakthrough entirely independent of anybody's help, especially the help of his inadvertent worst rival. Young died in 1829, and Robinson defends him to the end.

"We are made uneasy by those who effortlessly bridge several disciplines," he writes. "It is only too natural to regard them as dilettantes, or even to try to dismiss them as charlatans."

That Champollion was guilty of this kind of dismissal is probably beyond doubt. He wasn't a polymath like Young, but rather a tightly focused specialist who devoted his entire concentration to the field of Egyptian studies and gradually convinced himself that he'd needed nobody's insights but his own. He helped to head an expedition to Egypt in 1828 and lavished his fascination on this land of his dreams, where "absolute silence is necessary for me, to hear the voices of the ancestors".

The pace of his exertions - and the furnace heat of the Valley of Kings - broke his always tenuous health, and he died in Paris in 1832 at the age of 41. Robinson includes an absolutely fascinating concluding chapter on "The Hieroglyphics after Champollion", gently correcting the great pathfinder's mistakes while further impressing the reader with the scope of his accomplishments. It's a fitting final note to the best English-language account yet written of Champollion's tempestuous life.